59.1.119 problem 121

Internal problem ID [9291]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 121
Date solved : Monday, January 27, 2025 at 06:01:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} \left (1+x \right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 19

dsolve(3*x^2*(1+x)^2*diff(y(x),x$2)-x*(1-10*x-11*x^2)*diff(y(x),x)+(1+5*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {x^{{1}/{3}} c_{2} +c_{1} x}{\left (x +1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.242 (sec). Leaf size: 58

DSolve[3*x^2*(1+x)^2*D[y[x],{x,2}]-x*(1-10*x-11*x^2)*D[y[x],x]+(1+5*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \sqrt [6]{x} \left (3 c_2 x^{2/3}+2 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {4}{K[1]+1}-\frac {1}{3 K[1]}\right )dK[1]\right ) \]